The study investigates the relationship between radio and X-ray luminosity and black hole mass in both stellar mass and supermassive black holes. A sample of approximately 100 active galactic nuclei with measured black hole masses, 5 GHz core emission, and 2-10 keV luminosities, along with 8 galactic black holes with 50 simultaneous radio and X-ray observations, is analyzed. The results show a strong correlation between radio luminosity and both black hole mass and X-ray luminosity, defining a "fundamental plane" in three-dimensional space (log L_R, log L_X, log M) with the equation log L_R = (0.60 ± 0.11) log L_X + (0.78 ± 0.09) log M + 7.33 ± 4.05, and a scatter of σ_R = 0.88. This correlation is consistent with optically thin synchrotron emission from the jet for black holes accreting at less than a few percent of the Eddington rate. Radiatively inefficient accretion models agree well with the data. The study highlights the connection between accretion and jet processes, and provides constraints on the physical properties of the accretion flow from which the jet is launched. The results suggest that the observed correlation between radio and X-ray luminosity is a fundamental scaling of black hole activity, and that the physical properties of the accretion flow can be inferred from the observed correlation coefficients. The study also shows that the correlation between radio and X-ray luminosity is not only dependent on black hole mass but also on the accretion rate, and that the observed correlation coefficients can be used to constrain the accretion and jet physics. The findings have implications for understanding black hole activity in different regimes and for the broader study of black hole physics.The study investigates the relationship between radio and X-ray luminosity and black hole mass in both stellar mass and supermassive black holes. A sample of approximately 100 active galactic nuclei with measured black hole masses, 5 GHz core emission, and 2-10 keV luminosities, along with 8 galactic black holes with 50 simultaneous radio and X-ray observations, is analyzed. The results show a strong correlation between radio luminosity and both black hole mass and X-ray luminosity, defining a "fundamental plane" in three-dimensional space (log L_R, log L_X, log M) with the equation log L_R = (0.60 ± 0.11) log L_X + (0.78 ± 0.09) log M + 7.33 ± 4.05, and a scatter of σ_R = 0.88. This correlation is consistent with optically thin synchrotron emission from the jet for black holes accreting at less than a few percent of the Eddington rate. Radiatively inefficient accretion models agree well with the data. The study highlights the connection between accretion and jet processes, and provides constraints on the physical properties of the accretion flow from which the jet is launched. The results suggest that the observed correlation between radio and X-ray luminosity is a fundamental scaling of black hole activity, and that the physical properties of the accretion flow can be inferred from the observed correlation coefficients. The study also shows that the correlation between radio and X-ray luminosity is not only dependent on black hole mass but also on the accretion rate, and that the observed correlation coefficients can be used to constrain the accretion and jet physics. The findings have implications for understanding black hole activity in different regimes and for the broader study of black hole physics.